<< Chapter < Page Chapter >> Page >

Calculate final temperature from phase change: cooling soda with ice cubes

Three ice cubes are used to chill a soda at 20º C size 12{"20"°C} {} with mass m soda = 0.25  kg . The ice is at C and each ice cube has a mass of 6.0 g. Assume that the soda is kept in a foam container so that heat loss can be ignored. Assume the soda has the same heat capacity as water. Find the final temperature when all ice has melted.


The ice cubes are at the melting temperature of C . Heat is transferred from the soda to the ice for melting. Melting of ice occurs in two steps: first the phase change occurs and solid (ice) transforms into liquid water at the melting temperature, then the temperature of this water rises. Melting yields water at C , so more heat is transferred from the soda to this water until the water plus soda system reaches thermal equilibrium,

Q ice = Q soda . size 12{Q rSub { size 8{"ice"} } = - Q rSub { size 8{"soda"} } } {}

The heat transferred to the ice is Q ice = m ice L f + m ice c W ( T f C ) . The heat given off by the soda is Q soda = m soda c W ( T f 20º C ) . Since no heat is lost, Q ice = Q soda , so that

m ice L f + m ice c W T f C = - m soda c W T f 20º C .

Bring all terms involving T f size 12{T rSub { size 8{f} } } {} on the left-hand-side and all other terms on the right-hand-side. Solve for the unknown quantity T f size 12{T rSub { size 8{f} } } {} :

T f = m soda c W 20º C m ice L f ( m soda + m ice ) c W .


  1. Identify the known quantities. The mass of ice is m ice = 3 × 6.0  g = 0 . 018  kg size 12{m rSub { size 8{"ice"} } =3 "." 6`g=0 "." "018"`"kg"} {} and the mass of soda is m soda = 0 . 25  kg size 12{m rSub { size 8{"soda"} } =0 "." "25"`"kg"} {} .
  2. Calculate the terms in the numerator:
    m soda c W 20º C = 0 .25 kg 4186 J/kg ⋅º C 20º C = 20,930 J


    m ice L f = 0 . 018  kg 334,000  J/kg =6012  J. size 12{ ital "mL" rSub { size 8{f} } = left (0 "." "018"`"kg" right ) left ("333","000"`"J/kg" right )"=5995"`J} {}
  3. Calculate the denominator:
    m soda + m ice c W = 0 . 25  kg + 0 . 018 kg 4186 K/ ( kg ⋅º C =1122 J/º C . size 12{ left (m rSub { size 8{"ice"} } +m rSub { size 8{"soda"} } right )c rSub { size 8{W} } = left (0 "." "25"" kg+0" "." "018 kg" right ) left ("4186 K/" \( "kg" cdot °C right )"=1122 J/"°C} {}
  4. Calculate the final temperature:
    T f = 20 , 930 J 6012 J 1122 J/º C = 13º C.


This example illustrates the enormous energies involved during a phase change. The mass of ice is about 7 percent the mass of water but leads to a noticeable change in the temperature of soda. Although we assumed that the ice was at the freezing temperature, this is incorrect: the typical temperature is C . However, this correction gives a final temperature that is essentially identical to the result we found. Can you explain why?

We have seen that vaporization requires heat transfer to a liquid from the surroundings, so that energy is released by the surroundings. Condensation is the reverse process, increasing the temperature of the surroundings. This increase may seem surprising, since we associate condensation with cold objects—the glass in the figure, for example. However, energy must be removed from the condensing molecules to make a vapor condense. The energy is exactly the same as that required to make the phase change in the other direction, from liquid to vapor, and so it can be calculated from Q = mL v size 12{Q= ital "mL" rSub { size 8{f} } } {} .

The figure shows condensed water droplets on a glass of iced tea.
Condensation forms on this glass of iced tea because the temperature of the nearby air is reduced to below the dew point. The rate at which water molecules join together exceeds the rate at which they separate, and so water condenses. Energy is released when the water condenses, speeding the melting of the ice in the glass. (credit: Jenny Downing)

Real-world application

Energy is also released when a liquid freezes. This phenomenon is used by fruit growers in Florida to protect oranges when the temperature is close to the freezing point C . Growers spray water on the plants in orchards so that the water freezes and heat is released to the growing oranges on the trees. This prevents the temperature inside the orange from dropping below freezing, which would damage the fruit.

The figure shows bare tree branches covered with ice and icicles.
The ice on these trees released large amounts of energy when it froze, helping to prevent the temperature of the trees from dropping below C size 12{0°C} {} . Water is intentionally sprayed on orchards to help prevent hard frosts. (credit: Hermann Hammer)

Questions & Answers

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
Collins Reply
What is thermal heat all about
Abel Reply
why uniform circular motion is called a periodic motion?.
Boniface Reply
when a train start from A & it returns at same station A . what is its acceleration?
Mwdan Reply
what is distance of A to B of the stations and what is the time taken to reach B from A
the information provided is not enough
Hmmmm maybe the question is logical
where are the parameters for calculation
there is enough information to calculate an AVERAGE acceleration
mistake, there is enough information to calculate an average velocity
what is the unit of momentum
wha are the types of radioactivity ?
Worku Reply
what are the types of radioactivity
what is static friction
Golu Reply
It is the opposite of kinetic friction
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
I don't get it,if it's static then there will be no friction.
It means that static friction is that friction that most be overcome before a body can move
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
It is a force a body must overcome in order for the body to move.
If a particle accelerator explodes what happens
why we see the edge effect in case of the field lines of capacitor?
what is wave
Muhammed Reply
what is force
force is something which is responsible for the object to change its position
more technically it is the product of mass of an object and Acceleration produced in it
wave is disturbance in any medium
energy is distributed in any medium through particles of medium.
If a particle accelerator explodes what happens
Eboh Reply
we have to first figure out .... wats a particle accelerator first
What is surface tension
Subi Reply
The resistive force of surface.
Who can tutor me on simple harmonic motion
yusuf Reply
on both a string and peldulum?
Do you have a chit-chat contact
I dont have social media but i do have an email?
Which is
Where are you chatting from
I don't understand the basics of this group
teach him SHM init
Simple harmonic motion
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
syed Reply
definition of mass of conversion
umezurike Reply
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
how many topic are in physics
Praise what level are you
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Yeah basics of physics prin8
Heat nd Co for a level
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
please send the answer
the range of objects and phenomena studied in physics is
Bethel Reply
I don't know please give the answer
Practice Key Terms 3

Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?